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Question: How do I integrate int(1/(x-1)+sum((k+1)*x^k,k=0..2018)/sum(x^k,k=0..2019),x);

Question:How do I integrate int(1/(x-1)+sum((k+1)*x^k,k=0..2018)/sum(x^k,k=0..2019),x);

Thomas Dean 322 Maple 2020
October 09 2020
0

int(1/(x-1)+sum((k+1)*x^k,k=0..2018)/sum(x^k,k=0..2019),x);

Direct integration produces a large, messy statement, including numbers like 2017, 2016,...,1

Looking at the parts, the numbers 2020, 2019, etc. are in each.

(**) sum((k+1)*x^k,k=0..2018);
x^2019*(2019*x-2020)/(x-1)^2+1/(x-1)^2

(**) sum(x^k,k=0..2019);
x^2020/(x-1)-1/(x-1)

Looks like this should reduct to some simple expession????
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